In the technological world that we live in today, it always seems like smaller is better. Well in this case it is! With files getting ever more complicated, one way of saving space is the Haar Wavelet Transform. This saves space on your computer by compressing digital images and turning them into smaller files when being saved or transmitted on your computer. In this case a wavelet is a basis of a particular vector space and the basis is orthogonal. Pixels in digital pictures each have thier own entry into a very large matrix that can take up a lot of space on your computer if it wasn't compressed. What this process does is transform the original matrix so that some of the entries are zero; the more zero entries you have, the less space the matrix occupies on your computer. Without this application of Linear Algebra, we would all be spending a lot of money on lots of memory and huge hard drives to accommodate every thing that we have on our computers!

REFERENCES:

http://online.redwoods.cc.ca.us/instruct/darnold/laproj/Fall97/PMorton/imageComp3/sld001.htm

http://www.debugmode.com/imagecmp/